Find each exact function value.

tan π/3

Video transcript

Welcome back. I am so glad you're here. We're asked to determine the exact value of the given function. And our given function is the tangent of 11 pi divided by six. Our answer choices are answer choice, A the square root of three answer choice B negative square root three answer choice C negative square root three divided by three and answer choice D square root three divided by three. All right, we recall from previous lessons that 11 pi divided by six is an angle on the unit circle. So I'm going to draw a part of the unit circle real quick. Definitely check out the figure of the unit circle in your textbook. For one with all of the details, we've got a vertical Y axis and a horizontal X axis. They come together the origin in the middle. The unit circle lies over that every point on the unit circle is exactly one unit away from the origin. That's not true of what I drew. But you can imagine that it is 11 pi divided by six is an angle in the fourth quadrant. It's closer to the positive part of the X axis than the negative part of the Y axis in 11 pi divided by sixes xy coordinates are square root three divided by two negative one half. And we recall from previous lessons that the tangent of an angle theta is equal to Y divided by X. Well, we know the Y value and we know the X value so we can just do a little bit of algebra. The Y value is negative one half divided by the X value square at three divided by two. When we're dividing fractions, that's the same as multiplying by the reciprocal of the second fraction. So this is negative one half multiplied by two divided by the square root of three. Those twos cancel out and multiplying straight across, we have negative one divided by the square root of three. However, we want to rationalize this. So we're going to multiply both the numerator and the denominator by the square root of three in the numerator negative one multiplied by the square root of three is negative square root three divided by, in the denominator square root three, multiplied by itself is a positive three. And that is our exact value of the tangent of 11 pi divided by six. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.